Lecture 25-1 Aberrations Chromatic aberration Cameras, … correct nblue > nred Spherical aberration Parabolic mirrror Large telescopes, … Lecture 25-2 The Human Eye (1) ° Refraction at the cornea and lens surfaces produces an inverted real image on the retina of the eye (the brain interprets it upright !) ° For an object to be seen clearly, the image must be formed at the location of the retina ° The shape of the lens controls the distance of the image ≈ 2.5 cm Lecture 25 - 3 The Human Eye (2) • The lens is held in place by ligamen that connect it to the ciliary muscle that allows the lens to change shape and thus change the focus of the lens • The index of refraction of the two fluids in the eye are close to that of water with a value of 1.34; the index of refraction of the material making up the lens is 1.40 • Thus most of the refraction occurs at the air/cornea boundary. ≈ 2.5 cm Lecture 25-4 The Human Eye (3) ≈ 2.5 cm 111 += dd0 i f f depends on d0 d0 ↓ => f↓ to keep di at ≈ 2.5 cm Lecture 25-6 READING QUIZ 1 Which of the following statements is incorrect ? The statements describe the optical characteristics of the human eye. A| A near sighted eye focuses in front of the retina when observing an object located at infinity. B| A far sighted eye focuses behind the retina when observing an object located at infinity. C| A converging lens is used to correct the vision of a near sighted eye. D| Astigmatism is a condition where the eye does not have cylindrical symmetry about the central optical axis. E| A cataract operation of the second lens inside the eye removes the clouded lens and replaces it with a plastic implant. Lecture 25-5 Example: Corrective Lenses (1) Question: A hyperopic (far-sighted) person whose uncorrected near point is 75 cm wishes to read a newspaper at a distance of 25 cm. What is the power of the corrective lens needed for this person? Answer: • The corrective lens must produce a virtual, upright image of the newspaper at the near point of the person’s vision as shown below • The object and image are on the same side so the image distance is negative Lecture 25-6 Example: Corrective Lenses (2) • Thus the object distance is 25 cm and image distance is -75 cm 111 111 += +==+2.66 D 0.25 m- 0.75 m f dd0 i f • The required lens is a converging lens with a power of +2.66 diopters or +2.66 D (focal length of +0.376 m = 1/ 2.66 D) Lecture 25-21 Compound Microscope A microscope consists of two converging lenses: an objective (the front lens) and an eyepiece. An object is placed near the first focal point of the yL' objective. The separation of the lenses is adjusted so mo that the image produced by the objective is formed yfo just inside the first focal point of the eyepiece. The lateral magnification of the objective is xnp The eyepiece angular magnification (eye near point = xnp ) M e f e The overall magnifying power is defined as L xnp MmMoe foef Lecture 25-14 The Telescope • Like the microscope, telescopes come in many forms • First we will discuss (1) the refracting telescope and then (2) reflecting telescopes • The refracting telescope consists of two lenses – The objective lens and the eyepiece • In our example we represent the telescope using two thin lenses • However, an actual refracting telescope will use more sophisticated lenses Lecture 25-22 Astronomical Telescopes Refractor Telescope Same combination (except image at ∞) as compound microscope: Objective creates a real image which allows the eyepiece to magnify. The angular magnification M of the telescope is defined as θe /θo yy'' oe, fo fe f M eo o fe Lecture 25-15 Geometry of the Telescope • Because the object to be viewed is at a large distance, the incoming light rays can be thought of as being parallel (the object is at infinity) • The objective lens forms a real image of the distance object at distance fo • The eyepiece is placed so that the image formed by the objective is at distance fe from the eyepiece • The eyepiece forms a virtual, magnified image of the image formed by the objective • The image is at infinity, again producing parallel rays Lecture 25-16 Magnification of a Telescope • The magnification of the telescope is defined as the angle observed in the eyepiece, qe, divided by the angle subtended by the object being viewed, qo qeof mq =- =- qoef • Because the telescope deals with objects at very large distances, we cannot calculate the magnification of the telescope using the lens law • For example, one might try to express the magnification of the objective lens using the lens equation dd m =-ii =- =0 d Ñ o • We can still get the angular magnification, but we need to use angles rather than distances Lecture 25-17 Calculation of the Magnification of a Telescope (1) • Let’s calculate the angular magnification of a refracting telescope • The angle qo is the angle subtended by a distant object d qqooö=tan fo Lecture 25-18 Calculation of the Magnification of a Telescope (2) • The angle qe is the apparent angle seen in the eyepiece d qqö=tan eef e • The magnification is qeeodf/ f fo == Ω=- mq (inverted) qooedf/ f fe Lecture 25-19 Example: Refracting Telescope • The world’s largest refracting telescope was completed in 1897 and installed in Williams Bay, Wisconsin. It had an objective lens of diameter 40 inches (1.0 m) with a focal length of 62 feet (19 m). Question: What should the focal length of the eyepiece be to give a magnification of 250? Answer: fmo ==19 m 250 The 40-inch fo m = refracting telescope fe at Yerkes f 19 m Observatory f ==o =0.076 m = 7.6 cm e m 250 Lecture 25-20 Problems with Refracting Telescopes • The objective lens of a refracting telescope is large and heavy – The 40-inch refractor at Yerkes weighed 500 pounds • Supporting a large glass lens is difficult – Must be supported by its edges • Constructing large glass lenses is difficult • Glass lenses are thick and absorbe light • A glass lens has chromatic aberration – Different focal lengths for different colors • Solution: Replace the objective lens with a mirror Lecture 25-21 The Reflecting Telescope • Most large astronomical telescopes are reflecting telescopes with the objective lens being replaced with a concave mirror • Large mirrors are easier to fabricate and position than large lenses • The eyepiece is still a lens • Various types of reflecting telescopes have been developed • We will discuss three examples of the geometries of reflecting telescope – Reflector – Newtonian – Cassegrain Lecture 25-22 Basic Reflecting Telescope • Basic reflector • Replace the objective lens with a parabolic mirror • This design is impractical because the observer must be in the line of the incident light Lecture 25-23 Newtonian Reflecting Telescope • In 1670, Newton presented his design for a reflecting telescope to the Royal Society – The idea for a reflecting telescope came from James Gregory • Newton solved the observer problem by placing a small mirror that reflect the light out to an eyepiece • This mirror is small compared with the objective mirror and causes only a small loss of light from the image Lecture 25-24 Cassegrain Geometry for Reflecting Telescope • A further improvement on the geometry of the reflecting telescope is the Cassegrain geometry (named for the French sculptor Sieur Guillaume Cassegrain) first proposed in 1672 • Here a small mirror is used to reflect the image through a hole in the center of the objective mirror • This design and many improvements to this basic idea are the basis of modern astronomical telescopes Lecture 25-25 Reflector Telescope ‹ No chromatic aberration ‹ Large mirrors can be made (large amount of light gathered) ‹ Easier to support ‹ View center blocked off fo ‹ Maginfication m q =- fe (same as a refracting telescope) Whipple Telescope Lecture 25-26 The Hubble Space Telescope (1) • The Hubble Space Telescope (HST) was deployed April 25, 1990 from the Space Shuttle mission STS-31 • The HST orbits the Earth 590 km above the surface of the Earth, far above the atmosphere that disturbs the images gathered by ground-based telescopes • The HST is a Ritchey-Chrétien reflecting telescope arranged in a Cassegrain geometry Lecture 25-27 The Hubble Space Telescope (2) • The HST is a Ritchey-Chrétien reflecting telescope arranged in a Cassegrain geometry • This type of telescope uses a concave hyperbolic objective mirror rather than a spherical mirror and a convex hyperbolic secondary mirror • This arrangement gives the HST a wide field of view and eliminates spherical aberration • The objective mirror is 2.40 m in diameter and has an effective focal length of 57.6 m Lecture 25-28 Hubble Corrected • The original HST objective mirror was produced with a flaw caused by a defective testing instrument (deployed on April 25, 1990) • In December 1993, Space Shuttle Service Mission 1 (STS-61) deployed the COSTAR package that corrected the flaw in the objective mirror and allowed the HST to produce spectacular pictures • The two images of the galaxy M100 shown on the left and on the right demonstrate the image quality of the HST before and after the installation of COSTAR .